© 2010 Pearson Education, Inc. PowerPoint ® Lectures for College Physics: A Strategic Approach, Second Edition Chapter 2 Motion in One Dimension

© 2010 Pearson Education, Inc. Slide Motion in One Dimension

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© 2010 Pearson Education, Inc. Reading Quiz 1.The slope at a point on a position-versus-time graph of an object is A.the object’s speed at that point. B.the object’s average velocity at that point. C.the object’s instantaneous velocity at that point. D.the object’s acceleration at that point. E.the distance traveled by the object to that point. Slide 2-7

© 2010 Pearson Education, Inc. Answer 1.The slope at a point on a position-versus-time graph of an object is A.the object’s speed at that point. B.the object’s average velocity at that point. C.the object’s instantaneous velocity at that point. D.the object’s acceleration at that point. E.the distance traveled by the object to that point. Slide 2-8

© 2010 Pearson Education, Inc. Reading Quiz 2.The area under a velocity-versus-time graph of an object is A.the object’s speed at that point. B.the object’s acceleration at that point. C.the distance traveled by the object. D. the displacement of the object. E. This topic was not covered in this chapter. Slide 2-9

© 2010 Pearson Education, Inc. Answer 2.The area under a velocity-versus-time graph of an object is A.the object’s speed at that point. B.the object’s acceleration at that point. C.the distance traveled by the object. D. the displacement of the object. E. This topic was not covered in this chapter. Slide 2-10

© 2010 Pearson Education, Inc. Reading Quiz 3.A 1-pound ball and a 100-pound ball are dropped from a height of 10 feet at the same time. In the absence of air resistance A.the 1-pound ball hits the ground first. B.the 100-pound ball hits the ground first. C.the two balls hit the ground at the same time. D.There’s not enough information to determine which ball wins the race. Slide 2-11

© 2010 Pearson Education, Inc. Answer 3.A 1-pound ball and a 100-pound ball are dropped from a height of 10 feet at the same time. In the absence of air resistance A.the 1-pound ball hits the ground first. B.the 100-pound ball hits the ground first. C.the two balls hit the ground at the same time. D.There’s not enough information to determine which ball wins the race. Slide 2-12

© 2010 Pearson Education, Inc. Multiple Representations Motion diagram (student walking to school) Table of data Graph Slide 2-13

© 2010 Pearson Education, Inc. Review - Sign Conventions for Velocity  Velocity is a vector  It has both a magnitude and a direction  When we draw a velocity vector on a diagram, we use an arrow labeled with the symbol: ____ to represent the magnitude and direction.  For motion in one direction, vectors are restricted to point only “forward” or “backward” for horizontal motion (or “up” and “down” for vertical movement).  When we solve problems for motion along the x-axis, we use: _____.  For motion along the y-axis, we use: ____.

© 2010 Pearson Education, Inc. Review – Representing Velocity  We will use the symbol v, with no subscript, to represent the speed of an object  Remember: speed is the magnitude of the velocity vector and is always positive!  Velocity Equation (moving along x) OR (moving along y)

© 2010 Pearson Education, Inc. From position to velocity What do you does the slope of the graph represent? How many phases of motion are there in the diagram below?

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© 2010 Pearson Education, Inc. Stop & Think 2.1 pg. 36

© 2010 Pearson Education, Inc. Example Problem A car moves along a straight stretch of road. The graph below shows the car’s position as a function of time. (Note about “a versus b”) At what point (or points) do the following conditions apply? The displacement is zero. The speed is zero. The speed is increasing. The speed is decreasing. Slide 2-14

© 2010 Pearson Education, Inc. Translating position vs. time  velocity vs. time graphs  By finding and using the slope (rise over run), we can translate a position-versus- time graph into a velocity- versus-time graph!

© 2010 Pearson Education, Inc. Here is a motion diagram of a car moving along a straight stretch of road: Which of the following velocity-versus-time graphs matches this motion diagram? Checking Understanding A.B.C.D. Slide 2-17

© 2010 Pearson Education, Inc. Here is a motion diagram of a car moving along a straight stretch of road: Which of the following velocity-versus-time graphs matches this motion diagram? Answer A.B.C.D. Slide 2-18

© 2010 Pearson Education, Inc. Checking Understanding A graph of position versus time for a basketball player moving down the court appears like so: Which of the following velocity graphs matches the above position graph? A.B.C.D. Slide 2-19

© 2010 Pearson Education, Inc. A graph of position versus time for a basketball player moving down the court appears like so: Which of the following velocity graphs matches the above position graph? Answer A.B.C.D. Slide 2-20

© 2010 Pearson Education, Inc. A graph of velocity versus time for a hockey puck shot into a goal appears like so: Which of the following position graphs matches the above velocity graph? Checking Understanding A.B.C.D. Slide 2-21

© 2010 Pearson Education, Inc. A graph of velocity versus time for a hockey puck shot into a goal appears like so: Which of the following position graphs matches the above velocity graph? Answer A.B.C.D. Slide 2-22

© 2010 Pearson Education, Inc. What about reversing things?

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© 2010 Pearson Education, Inc. Acceleration Acceleration is: The rate of change of velocity The slope of a velocity-versus-time graph Slide 2-26

© 2010 Pearson Education, Inc. Free Fall Slide 2-36 “Looks like Mr. Galileo was correct…” -Apollo 15 astronaut David Scott

© 2010 Pearson Education, Inc. Free Fall Slide 2-36

© 2010 Pearson Education, Inc. Free Fall – Continued  Free fall is not restricted to objects that are “literally falling”.  Any object moving under the influence of gravity only, and no other forces, is in free fall!

© 2010 Pearson Education, Inc. Tennis balls are tested by measuring their bounce when dropped from a height of approximately 2.5 m. What is the final speed of a ball dropped from this height? Example Problem** Slide 2-34

© 2010 Pearson Education, Inc. An arrow is launched vertically upward. It moves straight up to a maximum height, then falls to the ground. The trajectory of the arrow is noted. Which choice below best represents the arrow’s acceleration at the different points? Checking Understanding A.A  E  B  D; C  0 B.E  D  C  B  A C.A  B  C  D  E D.A  B  D  E; C  0 Slide 2-37

© 2010 Pearson Education, Inc. An arrow is launched vertically upward. It moves straight up to a maximum height, then falls to the ground. The trajectory of the arrow is noted. Which choice below best represents the arrow’s acceleration at the different points? Answer A.A  E  B  D; C  0 B.E  D  C  B  A C.A  B  C  D  E D.A  B  D  E; C  0 Slide 2-38

© 2010 Pearson Education, Inc. Velocity to Position, One final note…  We know that we can find velocity by measuring the slope of a position graph.  If we have a velocity graph, we can find the position, not with slope, but by looking at the area under the graph. For example…

© 2010 Pearson Education, Inc. Motion with Constant Acceleration**  Example: Saturn V rocket  Double the acceleration of a Porsche!  3,000,000 kg vs 1480 kg  How fast is the rocket moving at the end of this acceleration and how far has it traveled?  We need new formulas!

© 2010 Pearson Education, Inc.

As you drive in your car at 15 m/s (just a bit under 35 mph), you see a child’s ball roll into the street ahead of you. You hit the breaks and stop as quickly as you can. In this case, you come to rest in 1.5 s. How far does your car travel as you brake to a stop?

© 2010 Pearson Education, Inc. A fully loaded Boeing 747 with all engines at full thrust accelerates at 2.6 m/s 2. Its minimum takeoff speed is 70 m/s. How much time will the plane take to reach its takeoff speed? What minimum length of runway does the plane require for takeoff?

© 2010 Pearson Education, Inc. Tennis balls are tested by measuring their bounce when dropped from a height of approximately 2.5 m. What is the final speed of a ball dropped from this height? Example Problem** Slide 2-34

© 2010 Pearson Education, Inc.